Analysis of Unsteady Aerodynamics of a Car Model with Radiator in Dynamic Pitching Motion using LS-DYNA

Transcription

1 Analyss of Unsteady Aerodynamcs of a Car Model wth Radator n Dynamc Ptchng Moton usng LS-DYNA Yusuke Nakae 1, Jro Takamtsu 1, Hrosh Tanaka 1, Tsuyosh Yasuk 1 1 Toyota Motor Corporaton 1 Introducton Recently, t s becomng clear that unsteady aerodynamc forces produced due to vehcle dynamc motons affect vehcle dynamc performance attrbutes such as straght-lne stablty or handlng characterstcs [1]. To clarfy the mpacts of these forces on vehcle dynamc performance attrbutes and ther mechansms, varous expermental researches are beng conducted. However, t s dffcult to measure these forces n wnd tunnel tests where a vehcle s statonary and s subected to a unform flow. Consequently, the detals of the phenomenon have yet to be clarfed. Numercal smulaton s expected to prove effectve n revealng the detaled mechansms of unsteady flow felds around vehcle n dynamc moton and ther mpacts on vehcle dynamc performance attrbutes. Nakae et al. [2] have conducted a numercal analyss of unsteady flow felds n the dynamc ptchng moton and the lane-change maneuverng of a smplfed car model smulatng a vehcle by applyng the Arbtrary Lagrangan-Euleran (ALE) method to a Large-Eddy Smulaton (LES) on an academc CFD code. Furthermore, Nakae et al. [3] have appled LS-DYNA ICFD solver to smlar analyss. Both studes concluded that the unsteady aerodynamc forces produced due to vehcle dynamc motons were mostly nduced by changes of flow structures around the front wheel house and under the car floor that changed wth vehcle moton. However, such numercal studes have been conducted on the smplfed scale car model that had no engne compartment and undersde components that seem to affect the flow felds. It s known that the coong-ar flow passng through engne compartment, radator, and outlets located n front wheel house and near the floor tunnel nterferes wth external flow. Ths nterference affects aerodynamc characterstcs of cars. Baeder et al. [4] have nvestgated coolng-ar nterference-effects on car models. They have shown that the surface pressure dstrbuton of the model was changed due to wth or wthout coolng-ar and also coolng-ar mass flow rate. Ths ndcates that to smulate unsteady flow felds around a vehcle n dynamc moton more precsely, nstallng engne compartment contanng a radator and undersde components onto a car model, and consderng the coolng-ar effects are needed. In ths study, numercal smulatons of the car models wthout or wth an engne compartment contanng a radator (.e. porous meda) n statonary state and n dynamc ptchng moton are performed usng new porous meda computng functon on LS-DYNA ICFD solver. The effects of the coong-ar flow passng through engne compartment on the unsteady aerodynamc forces and the flow felds are dscussed. And the necessty for nstallng engne compartment contanng a radator and undersde components onto a car model to get closer to actual car condtons s also shown. 2 Obect of ths study In ths secton, car models used n ths study, smulaton cases, and moton of the car model are shown. 2.1 Car model geometry To nvestgate the coolng-ar effects, two types of models shown n Fg. 1 were used. One has no engne compartment, undersde components, and the suspenson, same as the model n the lterature [3]. The other has engne compartment contanng a radator (.e. porous meda), front suspenson, and floor tunnel. Both of them are 1/4 scale car model. The models have a total length (L) of 1057 mm, a wdth (W) of 441 mm and a heght (H) of 373 mm. The model was obtaned by smoothng the body surface relatve to that of a real producton car. The tres and body are ndependent, and the varatons n the gap between the wheel houses and the tres when the vehcle s n dynamc moton were smulated (see Fg. 2). The porous property of the radator for the model wth engne compartment was defned usng Pressure-Velocty expermental data shown n Fg. 3.

2 (1) Model wthout Engne Compartment (2) Model wth Engne Compartment Fg.1: 1/4 scale car model Radator (Porous meda) Fg.2: Secton vew of wheel house Fg.3: Porous property of radator 2.2 Smulaton cases Table 1 shows the smulaton cases. The smulaton cases were made for two cases of statonary state and two ptchng moton cases. In all cases, manstream velocty was m/s, and the Reynolds number, whch s based on the total length of the model, was Re =1.91x10 6. To represent the ptchng moton, forced snusodal ptchng oscllaton was mposed on the model body usng the center of the wheel base as the center of rotaton (see Fg. 4). The effects of the coong-ar flow on the unsteady aerodynamc forces and the flow feld are examned by comparng the results of the above smulatons for the model wth engne compartment and wthout t. Table 1: Lst of smulaton case

3 3 Numercal method The ICFD solver on LS-DYNA was used n ths study. A Large-Eddy Smulaton (LES) was used to model turbulent components. And the Arbtrary Lagrangan-Euleran (ALE) method was used to represent the car model moton. Furthermore, the porous meda computng functon was also used to compute the flow feld n the radator. 3.1 Governng equatons A spatally fltered Naver-Stokes equaton (1) and a mass contnuty equaton (2) were used as the governng equatons, U U P U U U v sgs (1) t x x x x x U 0 (2) x where t, x, U, v, P, ρ, and μ respectvely represent, tme, coordnate components, velocty components, grd movement velocty components, pressure, ar densty, and the vscosty coeffcent. Varables marked wth a symbol are spatally fltered, whch means that they are grd scale component varables. Further, μ sgs s the sub grd scale turbulent eddy vscosty coeffcent and modeled by the Smagornsky model shown n equaton (3). The Smagornsky constant C S used n ths study s (3) sgs 2 CS fv 2SS C 0.18 (4) S In the above equatons, the rate of stran tensor S and the Van Drest wall dampng functon f v, Δ are defned as below. S 1 U 2 x U x y 1 exp 25 f v (6) Fg.4: Behavor of model n ptchng oscllaton (Case 3,4) 1 3 element volume (7) The y + s the non-dmensonal wall dstance. In the porous meda regon, coolng-ar drag by radator s added to the rght sde of the eq.(1) as external force D whch s calculated based on the Darcy-Forchhemer law. (5)

4 U t x U F U D U U P U U U v 1 1 sgs D x x x (9) Where ε, κ, and F respectvely represent, porosty, permeablty, and Forchhemer nerta parameter of porous meda. In ths study, ε was set to 1.0, κ and F were calculated based on the Pressure-Velocty expermental data shown n Fg. 3. Ansotropy of flows through radator by radator fns was not consdered. The fractonal step method was used to solve these equatons. 3.2 Valdaton of porous meda computaton Before conductng the smulatons of the car model wth radator, a valdaton of porous meda computng functon on LS-DYNA ICFD solver was carred out wth radator unt smulaton. The computatonal doman for ths valdaton s shown n Fg. 5. A radator s located at the mddle secton of the doman. Dmensons, characterstcs of the radator, and mesh sze around the radator are the same as those n the smulatons of the car model wth radator (Case 2,4). The ncomng wnd velocty mposed at nlet s shown n Fg.6. To valdate pressure dfferences (ΔP) between n front of a radator and behnd of t at varous wnd velocty, the ncomng wnd velocty was changed as tme progresses. x (8) Fg.5: Computatonal doman for valdaton of porous meda computaton Fg.6: Incomng wnd velocty Fg.7 shows the computatonal result of the pressure dfference (ΔP) between n front of the radator and behnd of t. The result showed the error wthn 5% from the theoretcal value. Ths ndcates the valdty of ths porous meda computng method. Error wthn 5% Fg.7: Comparson between result of computaton and theoretcal value

5 4 Numercal condtons Fg. 8 shows the computatonal doman for Case 1 through 4. Dmensons are ndcated n reference to L, the total length of the model. Flow drecton s 10L, wdth drecton s 2L and heght drecton s 1.5L. Fg. 9 shows the model surface and the computatonal grd n ts vcnty. The computatonal grd for the model surface has a resoluton of approxmately 4 mm, and a 5-layer boundary layer mesh was nserted n the model surface as well as n the floor of the computatonal doman. The frst layer has an approxmate heght of y + = 3.5. The entre computatonal doman conssts of unstructured tetrahedral grds usng a total of 13.6 mllon elements and 2.3 mllon nodes. Fg.8: Computatonal doman Fg.9: Close-up vew of computatonal grd Boundary condtons are presented n Table 2. They are the same across all smulaton cases. Table 2: Lst of boundary condton 5 Results In ths secton, the computatonal results for Case 1 through 4 are shown. Frstly, dfferences between flow felds around the car model wth engne compartment contanng the radator and that wthout engne compartment n statonary state are shown to reveal the effects of the coolng-ar flow passng through engne compartment. Secondly, dfference n unsteady aerodynamc force durng ptchng moton between these two models s showed. 5.1 Statonary case (Case 1 and 2) Fg. 10 through 14 respectvely show the dfferences between the car model wthout engne compartment (Case 1) and that wth engne compartment (Case 2) n the surface pressure dstrbuton on the upper and lower sde of the model body at the center cross-secton, the volume flow rate under the model body, the spatal averaged total pressure of each y-z plane under the model body, and the total pressure dstrbuton under the model body at a x-y plane. And also the results of the full scale real producton car whch s orgnal shape of the models n ths study wth opened radator grlle and closed grlle by another CFD code are shown smultaneously to valdate the results of ths computatons. The model of real producton car and CFD solver are the same as those n lterature [5]. Hood Cowl Hood Cowl (a) 1/4 scale car model (b) Real producton car Fg.10: Surface pressure dstrbuton on upper body at center cross-secton

6 k k Eng. Eng. compartment Floor tunnel compartment Floor tunnel (a) 1/4 scale car model (b) Real producton car Fg.11: Surface pressure dstrbuton on lower body at center cross-secton (a) 1/4 scale car model (b) Real producton car Fg.12: Volume flow rate under body (a) 1/4 scale car model (b) Real producton car Fg.13: Spatal averaged total pressure under body (a) 1/4 scale car model (b) Real producton car Fg.14: Total pressure dstrbuton under body

7 The results ndcate the tme averaged values for 0.7 second after suffcent convergence of the computatons. For the surface pressure dstrbuton on the upper sde (Fg.10), n the case of the model wth engne compartment, the hgher pressure on the engne hood and lower pressure on the wndsheld cowl than that on the model wthout engne compartment were observed. Remarkable dfferences n the surface pressure dstrbuton were observed on the lower sde of the model body (Fg. 11). In the case of the model wth engne compartment, sgnfcant hgher pressure on the front part (forward than x = 0.4) where the engne compartment s located was observed. Furthermore, lower pressure behnd there (behnd x = 0.4) where the floor tunnel s located was also observed. Ths sudden pressure change was occurred where the coolng-ar outlet (.e. the outlet located between rear end of the engne compartment and front end of the floor tunnel : n Fg. 11) s located. Other negatve pressure peaks located at x = 0.3 and 0.7 also correspond to the locaton of the outlet between bottom of the engne block and the front suspenson member ( n Fg. 11), and rear end of the floor tunnel (k n Fg.11) respectvely. The volume flow rate under the model body wth engne compartment decreased compared to the case of the model wthout engne compartment (Fg. 12). The total pressure under the model body wth engne compartment gradually decreased around x = 0.27 and drastcally decreased around x = 0.4 compared to the model wthout engne compartment (Fg. 13). The locatons where these changes occurred correspond to the locaton where the coolngar outlets mentoned n Fg. 11 are located. The total pressure dstrbuton under the model body wth engne compartment decreased from under the engne compartment. Especally, decreases from where the outlets are located were remarkable. These decreases correspond to Fg. 13. All of the dfferences between the model wth engne compartment and that wthout engne compartment descrbed above was also observed n the results of the real producton car wth opened radator grlle and closed grlle (Fg. 10(b) through 14(b)). 5.2 Dynamc case (Case 3 and 4) Fg. 15 shows the computatonal results for unsteady aerodynamc force durng the ptchng moton. The results ndcate the phase averaged value for fve cycles after suffcent convergence of the computatons. The most remarkable unsteadness n aerodynamc forces relatve to vehcle dynamc moton was observed n the lft force. Ths report focuses on the lft coeffcent C L whch seems to affect the vehcle dynamc performance attrbutes. The C L durng nose-down moton showed sgnfcant dfference whle t showed a consstent close correspondence durng nose-up moton between the model wth engne compartment and that wthout engne compartment. The C L actng on the model wth engne compartment showed hgher value than that wthout engne compartment only durng nose-down moton. Ths ndcates that evaluatons usng the car model wthout engne compartment have possbltes of overestmatng the ampltude of unsteady aerodynamc forces than the forces actng on a real producton car n dynamc moton. Fg.15: Unsteady aerodynamc force durng ptchng moton To pnpont the cause of the above-mentoned dfference n aerodynamc force, the C L actng on each part of the model body for nose-down at ptch angle 0 where the most remarkable dfference occured between the models ((A), (B) n Fg. 15) are presented n Fg. 16. These results revealed that the body

8 part whch have contrbuted to the ncrease n C L for the model wth engne compartment was most remarkably under the engne compartment and the front wheel house (FLR-1,FWH). 6 Dscusson In ths secton, the effects of the coong-ar flow passng through engne compartment on the flow felds and the unsteady aerodynamc force are dscussed. Through ths dscusson, the necessty for nstallng engne compartment contanng a radator and undersde components onto a car model to get closer to actual car condtons s also shown. 6.1 Statonary case (Case 1 and 2) As shown n secton 5.1, the surface pressure on the lower sde of the model body wth engne compartment obvously changed where the coolng-ar outlets are located. The upstream of the outlets, the surface pressure s hgher than that n downstream. Furthermore, the volume flow rate and the total pressure under the model body decreased from the locaton. These ndcate that the coong-ar flow passng through engne compartment obvously dsturbs (nterferes wth) the flow under the model body. And ths leads to the change of flow under the body and fnally affects the aerodynamc characterstcs of a car. These were also observed n the real producton car. Ths ndcates that to understand the flow felds around a vehcle more precsely, engne compartment and undersde components of a car should be consdered. 6.2 Dynamc case (Case 3 and 4) Fg.16: Aerodynamc force C L actng on each part of model body Consderng the coolng-ar effect revealed n prevous sectons, the causes underlyng the dfference n the C L durng nose-down moton ((A), (B) n Fg. 15) are examned. Fg. 17 shows the surface pressure dstrbuton on the model body for nose-down at ptch angle 0 ((A), (B) n Fg. 15). Same as shown n Fg. 16, remarkably hgher pressure was observed under the engne compartment and on the front wheel house of the model wth engne compartment than that of the model wthout engne compartment. Consequently, the total lft force C L actng on the model wth the engne compartment ndcates hgher value. In addton, dfference on the front fender panel especally behnd the front wheel house was also observed. (A) Wthout Eng. Compartment (B) Wth Eng. Compartment Fg.17: Surface pressure dstrbuton at ptch angle 0 durng node-down

9 Next comes an examnaton of the causes of the dfferences n the pressure dstrbuton under the engne compartment and on the front wheel house. Fg. 18 shows the velocty magntude dstrbuton at the center cross-secton and the x-y plane located 24mm above ground level. And Fg. 19 shows velocty magntude at y = and 24mm above ground level. In case of the model wth engne compartment, the flow velocty under the model body was remarkably lower. Ths orgnates from under the engne compartment especally the locatons where the coolng-ar outlets are located (.e. between rear end of the engne compartment and front end of the floor tunnel : n Fg. 18 and 19, between bottom of the engne block and the front suspenson member : n Fg. 18 and 19). Ths ndcates that the coolng-ar blowng from engne compartment dsturbs the flow under the model body and thus the flow s decelerated and pressure ncreases under the engne compartment. Moreover, n the engne compartment, pressure s orgnally hgher than that n external flow due to lower velocty of the flow n engne compartment. These two factors lead to ncreasng the surface pressure under the engne compartment and on the front wheel house as observed n Fg. 17. Consequently, the total lft force C L actng on the model wth the engne compartment ndcates hgher value. Lower velocty (A) Wthout Eng. Compartment (B) Wth Eng. Compartment Fg.18: Velocty magntude dstrbuton at ptch angle 0 durng node-down Fg.19: Velocty magntude at y = and 24 mm above ground level at ptch angle 0 durng node-down Fg. 20 shows the total pressure dstrbuton around front wheel house. The coolng-ar blowng from engne compartment also flows nto front wheel house and t affects the flow feld around front wheel house. In case of the model wth engne compartment, the flow blowng from the front wheel house to the outsde of the model body ncreases. Thus the wake regon of front wheel house wdens and t leads to decreasng the surface pressure on the front fender panel behnd the front wheel house as observed n Fg.17.

10 y z x (A) Wthout Eng. Compartment (B) Wth Eng. Compartment Fg.20: Total pressure dstrbuton around front wheel house at ptch angle 0 durng node-down Fg. 21 shows the stream lnes of the coong-ar flow passng through engne compartment and the radator for the model wth engne compartment. The flow out from the engne compartment strongly nterferes wth the external flow, especally wth the flow under the body. Consequently, the dfferences n the flow feld under the body occur and t greatly affects the aerodynamc characterstcs of cars. y z x y z x Fg.21: Coolng-arflow passng through engne compartment and radator at ptch angle 0 durng node-down These mechansms examned above are remarkably observed durng nose-down moton snce the flow under the model and the coolng-ar are accelerated due to the body moton. Whle durng the nose-up moton, the effect of the coolng-ar s comparatvely small snce the flow under the model and the coolng-ar are decelerated due to the body moton. 7 Summary The numercal smulatons of the car model wth an engne compartment contanng a radator (.e. porous meda) n statonary state and n dynamc ptchng moton were conducted usng new porous meda computng functon on LS-DYNA ICFD solver. As a result of ths study, the followngs were made clear.. The result of the porous meda computaton showed good agreement wth the theoretcal value. The valdty of the porous meda computng method was shown.. The effects of the coong-ar flow passng through engne compartment and radator on the flow felds and the unsteady aerodynamc force were clarfed.. The necessty for nstallng engne compartment contanng a radator and undersde components onto a car model to get closer to actual car condtons was shown. 8 Acknowledgments Thanks and apprecaton are extended to extensve assstance and support wth LS-DYNA provded by Mr. Amano and Mr. Hayash of the JSOL Corporaton over the course of ths study.

11 9 References [1] Okada, Y., et al., : "Flow Structures above the Trunk Deck of Sedan-Type Vehcles and Ther Influence on Hgh-Speed Vehcle Stablty 1st Report: On-Road and Wnd-Tunnel Studes on Unsteady Flow Characterstcs that Stablze Vehcle Behavor", SAE Techncal Paper, 2009, [2] Nakae, Y., et al., : "A Study of Unsteady Aerodynamc Forces Actng on Car n Dynamc Moton" Transactons of Socety of Automotve Engneers of Japan, 2013, Vol.44, No.6, [3] Nakae, Y., et al., : " Analyss of Unsteady Aerodynamcs of a Car Model n Dynamc ptchng Moton Usng LS-DYNA R7", 13th Internatonal LS-DYNA Users Conference, 2014 [4] Baeder, D., et al., : "Aerodynamc Investgaton of Vehcle Coolng-Drag", SAE Techncal Paper, 2012, [5] Tadatsu, M., et al., : "A Study on Aerodynamc Drag Reducton of Two-Box Vehcle" Transactons of Socety of Automotve Engneers of Japan, 2013, Vol.44, No.5,